Hyperstable polyphase adaptive IIR filters

This work considers the implementation of recursive identification algorithms based on hyperstability concepts with polyphase structures. It is shown that the strictly positive real (SPR) condition required for convergence of these schemes can always be met by using a sufficiently high polyphase expansion factor M. For a given M, the degree of persistent excitation required for parameter convergence is obtained. When a priori knowledge about the unknown system is available, a compensating filter can be designed to avoid the need for a high M.